SOLUTION: The twenty-third term in an arithmetic sequence is 2/3 and the fifty-third term in the sequence is 3/2. What is the thirty-fifth term?

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Question 1034883: The twenty-third term in an arithmetic sequence is 2/3 and the fifty-third term in the sequence is 3/2. What is the thirty-fifth term?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B35%5D+=+a%5B23%5D+%2B+12d+=+2%2F3+%2B+12d and a%5B35%5D+=+a%5B53%5D+-+18d+=+3%2F2+-+18d.
Subtract the first equation from the second equation, giving 5%2F6+-+30d+=+0, or d+=+1%2F36.
==> a%5B35%5D+=+a%5B23%5D+%2B+12d+=+2%2F3+%2B+12%2A%281%2F36%29+=+1